Question

The graph shown illustrates velocity versus time for two cars $A$ and $B$ constrained to move in a straight line. Both cars were at the same position at $t=0\text{s}$. Consider the following statements.
(1) Car $A$ is travelling west, and Car $B$ is travelling east.
(2) Car $A$ overtakes Car $B$ at $t=5\text{s}$
(3) Car $A$ overtakes Car $B$ at $t=10\text{s}$ .

Which of the following is correct?

• A. Only statement 1 is true
• B. Only statement 2 is true
• C. Only statement 3 is true
• D. Only statement 1 and 2 are true

Answer 1

The correct option is C Only statement 3 is true

Since for both velocities are positive, both are moving in the same direction.
The distance travelled is the magnitude of area under $v-t$ curve.
At $t=10\text{sec}$
Area under $v-t$ curve for car A, $A_A=\frac{1}{2}\times 10\times 10=50$ units.
Area under $v-t$ curve for car B, $A_B=\frac{1}{2}\times (7+3)\times 10=50$ units.
Since area for both cars is 50 units, therefore car $A$ will overtake car $B$ in $10\text{sec}$